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Solve the problem. Find the general solution of the homogen X1 + 2x2 3x3 = 0 4x1 + 7x29x3 = 0 -X1 - 3x2 + 6x3 = 0 Ox1 x2 = x3 3 x3 0 x1 -3 x2 = x3 3 1 x3 Ox1 x2 = x3 Ox1 -3 3 1 3 x2 = X3 -3 1 x3 2

Solve the problem. Find the general solution of the homogen X1 + 2x2 3x3 = 0 4x1 + 7x29x3 = 0 -X1 - 3x2 + 6x3 = 0 Ox1 x2 = x3 3 x3 0 x1 -3 x2 = x3 3 1 x3 Ox1 x2 = x3 Ox1 -3 3 1 3 x2 = X3 -3 1 x3 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Solving Homogeneous System of Linear Equations To solve the problem, we need to find the general solution of the homogeneous system of linear equations given below. The solution should be provided as a vector. #### System of Linear Equations: \[ \begin{aligned} &x_1 + 2x_2 - 3x_3 = 0 \\ &4x_1 + 7x_2 - 9x_3 = 0 \\ &-x_1 - 3x_2 + 6x_3 = 0 \\ \end{aligned} \] #### Answer Choices: 1. \[ \left[ \begin{array}{c} x_1 \\ x_2 \\ x_3 \\ \end{array} \right] = x_3 \left[ \begin{array}{c} -3 \\ 3 \\ 0 \\ \end{array} \right] \] 2. \[ \left[ \begin{array}{c} x_1 \\ x_2 \\ x_3 \\ \end{array} \right] = x_3 \left[ \begin{array}{c} -3 \\ 3 \\ 1 \\ \end{array} \right] \] (Correct Answer) 3. \[ \left[ \begin{array}{c} x_1 \\ x_2 \\ x_3 \\ \end{array} \right] = \left[ \begin{array}{c} -3 \\ 3 \\ 1 \\ \end{array} \right] \] 4. \[ \left[ \begin{array}{c} x_1 \\ x_2 \\ x_3 \\ \end{array} \right] = x_3 \left[ \begin{array}{c} 3 \\ -3 \\ 1 \\ \end{array} \right] \] Choose the correct vector that represents the general solution to the given system of linear equations.
Transcribed Image Text:### Solving Homogeneous System of Linear Equations To solve the problem, we need to find the general solution of the homogeneous system of linear equations given below. The solution should be provided as a vector. #### System of Linear Equations: \[ \begin{aligned} &x_1 + 2x_2 - 3x_3 = 0 \\ &4x_1 + 7x_2 - 9x_3 = 0 \\ &-x_1 - 3x_2 + 6x_3 = 0 \\ \end{aligned} \] #### Answer Choices: 1. \[ \left[ \begin{array}{c} x_1 \\ x_2 \\ x_3 \\ \end{array} \right] = x_3 \left[ \begin{array}{c} -3 \\ 3 \\ 0 \\ \end{array} \right] \] 2. \[ \left[ \begin{array}{c} x_1 \\ x_2 \\ x_3 \\ \end{array} \right] = x_3 \left[ \begin{array}{c} -3 \\ 3 \\ 1 \\ \end{array} \right] \] (Correct Answer) 3. \[ \left[ \begin{array}{c} x_1 \\ x_2 \\ x_3 \\ \end{array} \right] = \left[ \begin{array}{c} -3 \\ 3 \\ 1 \\ \end{array} \right] \] 4. \[ \left[ \begin{array}{c} x_1 \\ x_2 \\ x_3 \\ \end{array} \right] = x_3 \left[ \begin{array}{c} 3 \\ -3 \\ 1 \\ \end{array} \right] \] Choose the correct vector that represents the general solution to the given system of linear equations.
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